Approximation Algorithms for Survivable Multicommodity Flow Problems with Applications to Network Design

Multicommodity flow (MF) problems have a wide variety of applications in areas such as VLSI circuit design, network design, etc., and are therefore very well studied. The fractional MF problems are polynomial time solvable while integer versions are NP-complete. However, exact algorithms to solve the fractional MF problems have high computational complexity. Therefore approximation algorithms to solve the fractional MF problems have been explored in the literature to reduce their computational complexity. Using these approximation algorithms and the randomized rounding technique, polynomial time approximation algorithms have been explored in the literature. In the design of high-speed networks, such as optical wavelength division multiplexing (WDM) networks, providing survivability carries great significance. Survivability is the ability of the network to recover from failures. It further increases the complexity of network design and presents network designers with more formidable challenges. In this work we formulate the survivable versions of the MF problems. We build approximation algorithms for the survivable multicommodity flow (SMF) problems based on the framework of the approximation algorithms for the MF problems presented in [1] and [2]. We discuss applications of the SMF problems to solve survivable routing in capacitated networks.

Optimal multicommodity flow through the complete graph with random edge capacities

We consider a multicommodity flow problem on a complete graph whose edges have random, independent, and identically distributed capacities. We show that, as the number of nodes tends to infinity, the maximumutility, given by the average of a concave function of each commodity How, has an almost-sure limit. Furthermore, the asymptotically optimal flow uses only direct and two-hop paths, and can be obtained in a distributed manner.

Distributed flow algorithms for scalable similarity visualization

We describe simple yet scalable and distributed algorithms for solving the maximum flow problem and its minimum cost flow variant, motivated by problems of interest in objects similarity visualization. We formulate the fundamental problem as a convex-concave saddle point problem. We then show that this problem can be efficiently solved by a first order method or by exploiting faster quasi-Newton steps. Our proposed approach costs at most O(|ε|) per iteration for a graph with |ε| edges. Further, the number of required iterations can be shown to be independent of number of edges for the first order approximation method. We present experimental results in two applications: mosaic generation and color similarity based image layouting. © 2010 IEEE.

Distribution line models analysis for loss calculation within three-phase three-wire power flow algorithms

Three-phase three-wire power flow algorithms, as any tool for power systems analysis, require reliable impedances and models in order to obtain accurate results. Kron's reduction procedure, which embeds neutral wire influence into phase wires, has shown good results when three-phase three-wire power flow algorithms based on current summation method were used. However, Kron's reduction can harm reliabilities of some algorithms whose iterative processes need loss calculation (power summation method). In this work, three three-phase three-wire power flow algorithms based on power summation method, will be compared with a three-phase four-wire approach based on backward-forward technique and current summation. Two four-wire unbalanced medium-voltage distribution networks will be analyzed and results will be presented and discussed. © 2004 IEEE.

On the Scalability-Performance Tradeoffs in MPLS and IP Routing

MPLS (Multi-Protocol Label Switching) has recently emerged to facilitate the engineering of network traffic. This can be achieved by directing packet flows over paths that satisfy multiple requirements. MPLS has been regarded as an enhancement to traditional IP routing, which has the following problems: (1) all packets with the same IP destination address have to follow the same path through the network; and (2) paths have often been computed based on static and single link metrics. These problems may cause traffic concentration, and thus degradation in quality of service. In this paper, we investigate by simulations a range of routing solutions and examine the tradeoff between scalability and performance. At one extreme, IP packet routing using dynamic link metrics provides a stateless solution but may lead to routing oscillations. At the other extreme, we consider a recently proposed Profile-based Routing (PBR), which uses knowledge of potential ingress-egress pairs as well as the traffic profile among them. Minimum Interference Routing (MIRA) is another recently proposed MPLS-based scheme, which only exploits knowledge of potential ingress-egress pairs but not their traffic profile. MIRA and the more conventional widest-shortest path (WSP) routing represent alternative MPLS-based approaches on the spectrum of routing solutions. We compare these solutions in terms of utility, bandwidth acceptance ratio as well as their scalability (routing state and computational overhead) and load balancing capability. While the simplest of the per-flow algorithms we consider, the performance of WSP is close to dynamic per-packet routing, without the potential instabilities of dynamic routing.

A Study of feature extraction algorithms for optical flow tracking

Sparse optical flow algorithms, such as the Lucas-Kanade approach, provide more robustness to noise than dense optical flow algorithms and are the preferred approach in many scenarios. Sparse optical flow algorithms estimate the displacement for a selected number of pixels in the image. These pixels can be chosen randomly. However, pixels in regions with more variance between the neighbours will produce more reliable displacement estimates. The selected pixel locations should therefore be chosen wisely. In this study, the suitability of Harris corners, Shi-Tomasi's “Good features to track", SIFT and SURF interest point extractors, Canny edges, and random pixel selection for the purpose of frame-by-frame tracking using a pyramidical Lucas-Kanade algorithm is investigated. The evaluation considers the important factors of processing time, feature count, and feature trackability in indoor and outdoor scenarios using ground vehicles and unmanned aerial vehicles, and for the purpose of visual odometry estimation.

Mathematical decomposition technique applied to the probabilistic power flow problem

In this paper a framework based on the decomposition of the first-order optimality conditions is described and applied to solve the Probabilistic Power Flow (PPF) problem in a coordinated but decentralized way in the context of multi-area power systems. The purpose of the decomposition framework is to solve the problem through a process of solving smaller subproblems, associated with each area of the power system, iteratively. This strategy allows the probabilistic analysis of the variables of interest, in a particular area, without explicit knowledge of network data of the other interconnected areas, being only necessary to exchange border information related to the tie-lines between areas. An efficient method for probabilistic analysis, considering uncertainty in n system loads, is applied. The proposal is to use a particular case of the point estimate method, known as Two-Point Estimate Method (TPM), rather than the traditional approach based on Monte Carlo simulation. The main feature of the TPM is that it only requires resolve 2n power flows for to obtain the behavior of any random variable. An iterative coordination algorithm between areas is also presented. This algorithm solves the Multi-Area PPF problem in a decentralized way, ensures the independent operation of each area and integrates the decomposition framework and the TPM appropriately. The IEEE RTS-96 system is used in order to show the operation and effectiveness of the proposed approach and the Monte Carlo simulations are used to validation of the results. © 2011 IEEE.

Maximizing transported data in a wireless sensor network: how much can the network transport before partition?

We consider a scenario where the communication nodes in a sensor network have limited energy, and the objective is to maximize the aggregate bits transported from sources to respective destinations before network partition due to node deaths. This performance metric is novel, and captures the useful information that a network can provide over its lifetime. The optimization problem that results from our approach is nonlinear; however, we show that it can be converted to a Multicommodity Flow (MCF) problem that yields the optimal value of the metric. Subsequently, we compare the performance of a practical routing strategy, based on Node Disjoint Paths (NDPs), with the ideal corresponding to the MCF formulation. Our results indicate that the performance of NDP-based routing is within 7.5% of the optimal.

A geometric mass-preserving redistancing scheme for the level set function

In this paper we describe and evaluate a geometric mass-preserving redistancing procedure for the level set function on general structured grids. The proposed algorithm is adapted from a recent finite element-based method and preserves the mass by means of a localized mass correction. A salient feature of the scheme is the absence of adjustable parameters. The algorithm is tested in two and three spatial dimensions and compared with the widely used partial differential equation (PDE)-based redistancing method using structured Cartesian grids. Through the use of quantitative error measures of interest in level set methods, we show that the overall performance of the proposed geometric procedure is better than PDE-based reinitialization schemes, since it is more robust with comparable accuracy. We also show that the algorithm is well-suited for the highly stretched curvilinear grids used in CFD simulations. Copyright (C) 2010 John Wiley & Sons, Ltd.

Iterative strong coupling of dimensionally heterogeneous models

In this article we address decomposition strategies especially tailored to perform strong coupling of dimensionally heterogeneous models, under the hypothesis that one wants to solve each submodel separately and implement the interaction between subdomains by boundary conditions alone. The novel methodology takes full advantage of the small number of interface unknowns in this kind of problems. Existing algorithms can be viewed as variants of the `natural` staggered algorithm in which each domain transfers function values to the other, and receives fluxes (or forces), and vice versa. This natural algorithm is known as Dirichlet-to-Neumann in the Domain Decomposition literature. Essentially, we propose a framework in which this algorithm is equivalent to applying Gauss-Seidel iterations to a suitably defined (linear or nonlinear) system of equations. It is then immediate to switch to other iterative solvers such as GMRES or other Krylov-based method. which we assess through numerical experiments showing the significant gain that can be achieved. indeed. the benefit is that an extremely flexible, automatic coupling strategy can be developed, which in addition leads to iterative procedures that are parameter-free and rapidly converging. Further, in linear problems they have the finite termination property. Copyright (C) 2009 John Wiley & Sons, Ltd.

A high-resolution soil erosion risk map of Switzerland as strategic policy support system

Soil erosion models and soil erosion risk maps are often used as indicators to assess potential soil erosion in order to assist policy decisions. This paper shows the scientific basis of the soil erosion risk map of Switzerland and its application in policy and practice. Linking a USLE/RUSLE-based model approach (AVErosion) founded on multiple flow algorithms and the unit contributing area concept with an extremely precise and high-resolution digital terrain model (2 m × 2 m grid) using GIS allows for a realistic assessment of the potential soil erosion risk, on single plots, i.e. uniform and comprehensive for the agricultural area of Switzerland (862,579 ha in the valley area and the lower mountain regions). The national or small-scale soil erosion prognosis has thus reached a level heretofore possible only in smaller catchment areas or single plots. Validation was carried out using soil loss data from soil erosion damage mappings in the field from long-term monitoring in different test areas. 45% of the evaluated agricultural area of Switzerland was classified as low potential erosion risk, 12% as moderate potential erosion risk, and 43% as high potential erosion risk. However, many of the areas classified as high potential erosion risk are located at the transition from valley to mountain zone, where many areas are used as permanent grassland, which drastically lowers their current erosion risk. The present soil erosion risk map serves on the one hand to identify and prioritise the high-erosion risk areas, and on the other hand to promote awareness amongst farmers and authorities. It was published on the internet and will be made available to the authorities in digital form. It is intended as a tool for simplifying and standardising enforcement of the legal framework for soil erosion prevention in Switzerland. The work therefore provides a successful example of cooperation between science, policy and practice.

Optimización de una energía mediante cortes de grafos. Segmentación de imágenes

La segmentación de imágenes puede plantearse como un problema de minimización de una energía discreta. Nos enfrentamos así a una doble cuestión: definir una energía cuyo mínimo proporcione la segmentación buscada y, una vez definida la energía, encontrar un mínimo absoluto de la misma. La primera parte de esta tesis aborda el segundo problema, y la segunda parte, en un contexto más aplicado, el primero. Las técnicas de minimización basadas en cortes de grafos permiten obtener el mínimo de una energía discreta en tiempo polinomial mediante algoritmos de tipo min-cut/max-flow. Sin embargo, estas técnicas solo pueden aplicarse a energías que son representabas por grafos. Un importante reto es estudiar qué energías son representabas así como encontrar un grafo que las represente, lo que equivale a encontrar una función gadget con variables adicionales. En la primera parte de este trabajo se estudian propiedades de las funciones gadgets que permiten acotar superiormente el número de variables adicionales. Además se caracterizan las energías con cuatro variables que son representabas, definiendo gadgets con dos variables adicionales. En la segunda parte, más práctica, se aborda el problema de segmentación de imágenes médicas, base en muchas ocasiones para la diagnosis y el seguimiento de terapias. La segmentación multi-atlas es una potente técnica de segmentación automática de imágenes médicas, con tres aspectos importantes a destacar: el tipo de registro entre los atlas y la imagen objetivo, la selección de atlas y el método de fusión de etiquetas. Este último punto puede formularse como un problema de minimización de una energía. A este respecto introducimos dos nuevas energías representables. La primera, de orden dos, se utiliza en la segmentación en hígado y fondo de imágenes abdominales obtenidas mediante tomografía axial computarizada. La segunda, de orden superior, se utiliza en la segmentación en hipocampos y fondo de imágenes cerebrales obtenidas mediante resonancia magnética. ABSTRACT The image segmentation can be described as the problem of minimizing a discrete energy. We face two problems: first, to define an energy whose minimum provides the desired segmentation and, second, once the energy is defined we must find its global minimum. The first part of this thesis addresses the second problem, and the second part, in a more applied context, the first problem. Minimization techniques based on graph cuts find the minimum of a discrete energy in polynomial time via min-cut/max-flow algorithms. Nevertheless, these techniques can only be applied to graph-representable energies. An important challenge is to study which energies are graph-representable and to construct graphs which represent these energies. This is the same as finding a gadget function with additional variables. In the first part there are studied the properties of gadget functions which allow the number of additional variables to be bounded from above. Moreover, the graph-representable energies with four variables are characterised and gadgets with two additional variables are defined for these. The second part addresses the application of these ideas to medical image segmentation. This is often the first step in computer-assisted diagnosis and monitoring therapy. Multiatlas segmentation is a powerful automatic segmentation technique for medical images, with three important aspects that are highlighted here: the registration between the atlas and the target image, the atlas selection, and the label fusion method. We formulate the label fusion method as a minimization problem and we introduce two new graph-representable energies. The first is a second order energy and it is used for the segmentation of the liver in computed tomography (CT) images. The second energy is a higher order energy and it is used for the segmentation of the hippocampus in magnetic resonance images (MRI).

Development of a conceptual model of the soil-moisture-plant sub-system of the hydrological cycle

The soil-plant-moisture subsystem is an important component of the hydrological cycle. Over the last 20 or so years a number of computer models of varying complexity have represented this subsystem with differing degrees of success. The aim of this present work has been to improve and extend an existing model. The new model is less site specific thus allowing for the simulation of a wide range of soil types and profiles. Several processes, not included in the original model, are simulated by the inclusion of new algorithms, including: macropore flow; hysteresis and plant growth. Changes have also been made to the infiltration, water uptake and water flow algorithms. Using field data from various sources, regression equations have been derived which relate parameters in the suction-conductivity-moisture content relationships to easily measured soil properties such as particle-size distribution data. Independent tests have been performed on laboratory data produced by Hedges (1989). The parameters found by regression for the suction relationships were then used in equations describing the infiltration and macropore processes. An extensive literature review produced a new model for calculating plant growth from actual transpiration, which was itself partly determined by the root densities and leaf area indices derived by the plant growth model. The new infiltration model uses intensity/duration curves to disaggregate daily rainfall inputs into hourly amounts. The final model has been calibrated and tested against field data, and its performance compared to that of the original model. Simulations have also been carried out to investigate the effects of various parameters on infiltration, macropore flow, actual transpiration and plant growth. Qualitatively comparisons have been made between these results and data given in the literature.

Active flow control bump design using hybrid Nash-game coupled to evolutionary algorithms

In this paper, the optimal design of an active flow control device; Shock Control Bump (SCB) on suction and pressure sides of transonic aerofoil to reduce transonic total drag is investigated. Two optimisation test cases are conducted using different advanced Evolutionary Algorithms (EAs); the first optimiser is the Hierarchical Asynchronous Parallel Evolutionary Algorithm (HAPMOEA) based on canonical Evolutionary Strategies (ES). The second optimiser is the HAPMOEA is hybridised with one of well-known Game Strategies; Nash-Game. Numerical results show that SCB significantly reduces the drag by 30% when compared to the baseline design. In addition, the use of a Nash-Game strategy as a pre-conditioner of global control saves computational cost up to 90% when compared to the first optimiser HAPMOEA.